Even in the immediate aftermath of a painful defeat, it would be wholly unwise for a manager to offer direct criticism to his board of directors. Dangerous to his job security, in fact.

Neil Lennon was clearly aware of that much upon Celtic being bundled out of Europe by Milan on Tuesday. The Northern Irishman was philosophical when assessing Celtic's troubles in Group H, while offering the occasional intriguing insight, rather than be in any way confrontational.

Still, should Celtic's power brokers ever take exception to a Lennon analysis, they would be wise to glance at recent history. Directors always look better against the backdrop of a winning team. This term, as Celtic have toiled in the Champions League, it is reasonable to ask why.

When the board hold balance sheets aloft it should be remembered that Lennon's role in such figures – both by way of successive Champions League participation and player sales after development – has been crucial. To the tune of tens of millions, to be precise. And, make no mistake, those in charge of Celtic are not slow in shouting from the rooftops. That much was illustrated by the chairman, Ian Bankier, at the recent annual meeting. He said: "The momentum we've built up in the last three to five years is formidable. With luck on our side and success on the field, we will be nothing short of unstoppable."

By quarter to 10 on Tuesday, with not even Europa League football secured into the new year, that "unstoppable" comment seemed as laughable as it was badly timed.

Should Lennon feel frustration after this season's woe, as he would be fully entitled to, it would also be wise of his superiors to take heed. The manager has not been handed a particularly adequate set of tools, a matter that was apparent even at the Champions League's qualifying stage. Lennon touched only briefly on the topic of recruitment after Milan's 3-0 win in Glasgow. His point was a straightforward one; that it will have to improve if Celtic are to continue to compete in the Champions League.

The appearance of Milan, a side of vastly superior quality to Celtic, was not required for that to be known. Celtic signed two strikers in the summer, Amido Baldé and Teemu Pukki, who were not deemed worthy of stepping from the substitutes' bench. Pukki, a Finland international, has proved to be a particular disappointment.

Other than Gary Hooper, who was targeted specifically by Lennon within weeks of taking office, Celtic have struggled to secure strong centre forwards. In the context of Celtic's history, that is an anomaly. It is also obvious week on week in domestic football, where there is enough leeway for Celtic to routinely get away with it.

Other transfer arrivals have looked long-term projects, which carries an obvious danger when facing off against Europe's top teams. Milan, who arrived in Glasgow as a club in crisis, left having swatted aside a team who missed glaring chances and defended in woeful fashion. Even when Celtic were lauded after September's loss in San Siro, it should have been recognised that they totally lacked conviction in front of goal.

The Celtic board would bridle at any suggestion they are down-sizing and point to the Scottish environment as restrictive, but it is difficult to look at Lennon's team in comparison with a year ago and claim any progress has been made. Celtic's one defensive substitute for Milan's visit was a 20-year-old, who has started only two first-team games. In a business sense, some argue it would be folly for Celtic to speculate more than is already the case. Football is a volatile environment, after all, and Celtic have known dark times in the past. There can also be no automatic guarantee that signing certain players means success.

Yet it would offer a better chance and, pertinently, show supporters who stump up cash in their tens of thousands that their club has genuine aspirations to improve. When Celtic reached the Champions League knockout phase last season, there was no reason whatsoever to regard that as a one-off opportunity. With finances strong and the domestic scene taken care of until such time as Rangers sort themselves out, Celtic had a genuine opportunity to re-establish themselves as a regular European force. Instead, their squad has regressed.

Recruitment aside, Celtic should surely look to produce the best developing talent in Scotland. Instead, only James Forrest has emerged from the club's youth set-up in recent times to command a regular first-team place. Were the first team filled with superb, expensive imports, that would at least be understandable.

As top clubs in England and overseas circle around Ryan Gauld at Dundee United, it is legitimate to ask why Celtic did not make genuine moves to secure an outstanding prospect who has been known on the Scottish scene for years. Celtic can hardly lay claim to be producing better themselves.

What must also be recognised is that players Lennon has been left with and relies upon have let him down. Georgios Samaras and Kris Commons have been dismal in the group stage of the Champions League. Both have been championed by Lennon for next to no return in Group H. Scott Brown did his bit to undermine the entire campaign with a petulant kick on Neymar which landed him a three-match suspension. With so little resource elsewhere, Lennon could ill afford these problems.

A year ago, he was being touted as hot managerial property as Celtic rose to European prominence. He had shown a clear aptitude for developing the likes of Hooper, Victor Wanyama and Fraser Forster, while placing a winning team on the pitch. Forster, it seems inevitable, played his last home Champions League game for Celtic on Tuesday.

Like the players he works with, Lennon has ambition. Given how much he has contributed to Celtic, not least financially, it would be sad if that needs to be realised elsewhere.